Polyhedral Formulations and Loop Elimination Constraints for Distribution Network Expansion Planning

Distribution network expansion planning (DNEP) aims at minimizing the capital and operational cost of the expansion plan; the plan entails choosing conductor types and line construction routes together with substation installation and reinforcement that allow serving the demand while satisfying the physical and technical constraints of the expanded network. Two findings are reported in this paper. First, DNEP can be exactly formulated as a disjunctive conic program, in two equivalent formulations; both formulations admit a tight polyhedral approximation and can be solved for the globally optimal solution using software for mixed-integer linear programming (MILP). Second, the DNEP solution can be computed more efficiently when the linear relaxations of the MILP formulations are strengthened using loop elimination constraints. Numerical results on practical DNEP problems reveal that combining the parallel equivalent-circuit polyhedral formulation with the spanning tree loop elimination constraints yields MILP planning solutions with a tight relative optimality gap and within reasonable computing time. In addition, the results are at least of the same quality if not better than those reported in the recent literature.